Horizontal Projectile Motion
Calculate horizontal projectile motion using initial velocity and height. Get time of flight, range, final velocity, and impact angle with interactive charts.
About This Calculator
The Horizontal Projectile Motion Calculator helps you solve physics problems involving objects launched horizontally from an elevated position. This tool computes the time of flight, horizontal range, final velocity components, and impact angle using standard kinematic equations with the gravitational constant g = 9.80665 m/s². It is ideal for students studying kinematics, teachers preparing problem sets, and anyone working through introductory physics exercises.
The calculator applies the fundamental equations of motion for a projectile launched with purely horizontal initial velocity. Since there is no initial vertical velocity component, the time of flight depends solely on the drop height and gravity (t = √(2h/g)). The horizontal range is then the product of initial velocity and time of flight (R = v₀ × t). The final velocity combines the constant horizontal component with the vertical component gained during the fall (v_y = g × t). The trajectory follows a parabolic path described by y = h − (g × x²) / (2 × v₀²).
Key Formulas
Time of Flight: t = √(2h / g)
Horizontal Range: R = v₀ × t
Final Vertical Velocity: v_y = g × t
Final Velocity: v = √(v₀² + v_y²)
Impact Angle: θ = arctan(v_y / v₀)
Trajectory: y = h − gx² / (2v₀²)
How to Use
Enter the initial horizontal velocity in meters per second (m/s) and the launch height in meters (m). Click Calculate to see the time of flight, horizontal distance traveled, velocity components at impact, and the full parabolic trajectory. The chart tab switches between a summary bar chart and a trajectory height distribution view.
About Projectile Motion
Horizontal projectile motion is one of the classic problems in kinematics taught in high school and college physics. The key insight is that horizontal and vertical motions are independent — gravity only affects the vertical component, while horizontal velocity remains constant (ignoring air resistance). This principle was famously demonstrated by Galileo and forms the foundation for understanding more complex projectile problems with launch angles.
Frequently Asked Questions
What is horizontal projectile motion?
Horizontal projectile motion describes the motion of an object launched horizontally from an elevated position. It has constant horizontal velocity (no horizontal acceleration) and constant downward acceleration due to gravity, following a parabolic trajectory until it hits the ground.
How do you calculate the time of flight for horizontal projectile motion?
Time of flight is calculated using t = √(2h/g), where h is the initial height and g is the gravitational acceleration (9.80665 m/s²). The horizontal velocity does not affect the time it takes to fall — only the initial height and gravity matter.
How do you calculate the horizontal range of a projectile?
Horizontal range is calculated as R = v₀ × t, where v₀ is the initial horizontal velocity and t is the time of flight. The range increases linearly with initial velocity and with the square root of initial height.
What is the trajectory equation for horizontal projectile motion?
The trajectory equation is y = h − (g × x²) / (2 × v₀²), where h is the initial height, g is gravity, x is the horizontal distance from launch, and v₀ is the initial horizontal velocity. This describes a parabolic path.
What is the impact angle of a horizontally launched projectile?
The impact angle is calculated as θ = arctan(v_y / v₀), where v_y = g × t is the final vertical velocity and v₀ is the initial horizontal velocity. The angle increases with higher drop height and lower initial velocity.
Does air resistance affect horizontal projectile motion?
This calculator assumes no air resistance, as is standard in introductory physics. In real-world scenarios, air resistance reduces both horizontal range and final velocity. The equations here are ideal for physics problem-solving and educational purposes.